Решите уравнение 2cos 2x+(cos x-cos 3x)/(cos x+cos 3x)=2.

2cos 2x+(cos x-cos 3x)/(cos x+cos 3x)=2(cos x-cos 3x)/(cos x+cos 3x)-4sin^2 x=0 (sin xsin 2x)/(cos xcos 2x)-4sin^2 x=0(sin^2 xcos x(2-4cos 2x))/(cos xcos 2x)=0 [arraylsin x=0 cos 2x=(1)/(2)array.[arraylx=kpi 2x=+-(pi)/(3)+2kpiarray., kinZ[arraylx=kpi x=+-(pi)/(6)+kpiarray., kinZ.

\(x=k\pi,\ \pm\frac{\pi}{6}+k\pi,\ k\in\mathbb{Z}\)